# American Institute of Mathematical Sciences

March  2021, 6(1): 1-22. doi: 10.3934/puqr.2021001

## G-Lévy processes under sublinear expectations

 1 Zhongtai Securities Institute for Financial Studies, Shandong University, Jinan 250100, Shandong, China 2 School of Mathematics, Shandong University, Jinan 250100, Shandong, China

Email: humingshang@sdu.edu.cn, peng@sdu.edu.cn

Received  June 22, 2020 Accepted  December 14, 2020 Published  March 2021

Fund Project: This work was supported by National Key R&D Program of China (Grant No. 2018YFA0703900), National Natural Science Foundation of China (Grant No. 11671231) , Tian Yuan Fund of the National Natural Science Foundation of China (Grant Nos. 11526205 and 11626247) and National Basic Research Program of China (973 Program) (Grant No. 2007CB814900).

We introduce G-Lévy processes which develop the theory of processes with independent and stationary increments under the framework of sublinear expectations. We then obtain the Lévy–Khintchine formula and the existence for G-Lévy processes. We also introduce G-Poisson processes.

Citation: Mingshang Hu, Shige Peng. G-Lévy processes under sublinear expectations. Probability, Uncertainty and Quantitative Risk, 2021, 6 (1) : 1-22. doi: 10.3934/puqr.2021001
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